Related papers: Maximum principles for the relativistic heat equat…
Close to equilibrium, the excess heat governs the static fluctuations. We study the heat capacity in that McLennan regime, i.e., in linear order around equilibrium, using an expression in terms of the average energy that extends the…
We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the…
As of now, an optimal quantum algorithm solving partial differential equations eludes us. There are several different methods, each with their own strengths and weaknesses. In past years comparisons of these existing methods have been made,…
We show that a pair of conjectures raised in [11] concerning the construction of normal solutions to the relativistic Boltzmann equation are valid. This ensures that the results in [11] hold for any range of positive temperatures and that…
Relativistic transport phenomena are important from both theoretical and practical point of view. Accordingly, hydrodynamics of relativistic gas has been extensively studied theoretically. Here, we introduce a three-dimensional canonical…
The principle called information causality has been used to deduce Tsirelson's bound. In this paper we derive information causality from monotonicity of divergence and relate it to more basic principles related to measurements on…
We study the Radiative Transfer equations coupled with the time dependent temperature equation of a fluid: existence, uniqueness, a maximum principle are established. A short numerical section illustrates the pros and cons of the method.
In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat…
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented.…
The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a…
An analysis of efficiency and its bounds at maximum work output for Carnot-like heat engines is conducted. The heat transfer processes are described by the linear law with time-dependent heat conductance. The upper bound of efficiency is…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
The weak and strong comparison principles, respectively, are investigated for quasi-linear elliptic boundary value problems with the $p$-Laplacian in one space dimension. We treat the degenerate case of $2 < p < \infty$ and allow also for…
In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the fractional Laplace operator as a special case). A weak…
The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid-gas coexistence in heat conduction.…
In this paper, we study a certain approximation property for a time optimal control problem of the heat equation with $L^\infty$-potential. We prove that the optimal time and the optimal control to the same time optimal control problem for…
Within the emerging field of quantum thermodynamics the issues of heat transfer and heat rectification are basic ingredients for the understanding and design of heat engines or refrigerators at nanoscales. Here, a consistent and versatile…
Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess positive entire solutions) guarantee optimal universal estimates of solutions of related initial and…